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Journal of Lie Theory 31 (2021), No. 2, 439--458
Copyright Heldermann Verlag 2021

Classification of Finite Dimensional Nilpotent Lie Superalgebras by their Multipliers

Saudamini Nayak
Institute of Mathematics and Applications, Bhubaneswar, India


Let $L$ be a nilpotent Lie superalgebra of dimension $(m\mid n)$ and $$ s(L) = \frac{1}{2}[(m + n - 1)(m + n -2)]+ n+ 1 - \dim \mathcal{M}(L), $$ where $\mathcal{M}(L)$ denotes the Schur multiplier of $L$. Here $s(L)\geq 0$ and the structure of all non-abelian nilpotent Lie superalgebras with $s(L)=0$ is known from a previous publication of the author [{\em Multipliers of nilpotent Lie superalgebras}, Comm. Algebra 47/2 (2019) 689--705]. This paper is devoted to obtain all nilpotent Lie superalgebras $L$ when $s(L) \leq 2$. Further, we apply those results to list all non-abelian nilpotent Lie superalgebras $L$ with $ t(L) \leq 4$.

Keywords: Nilpotent Lie superalgebra, multiplier, special Heisenberg Lie superalgebra.

MSC: 17B30; 17B05.

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